Question

If we reject a hypothesized value because it differs from the sample statistic by more than...

If we reject a hypothesized value because it differs from the sample statistic by more than 1.75 standard errors, what is the probability that we have rejected a hypothesis that is actually true?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Answer: probability = 0.0401

Explanation:

A Type I error is defined as the probability of rejecting the null hypothesis when the null hypothesis is actually TRUE”. In a statistical test analysis, it is defined as the p-value (or the observed significance level).

The hypothesized value differs from the sample statistic by more than 1.75 standard errors which means the standardized test statistic (z statistic) of the test is 1.75

The p-value for the z statistic is obtained from the z distribution table for z = 1.75 (In excel use function =1-NORM.S.DIST(1.75,TRUE))

P-value = 0.040059

Hence there is approximately 4% chance that the null hypothesis is rejected when the null hypothesis is actually TRUE

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In hypothesis testing, which statement is true? A. if we reject the alternate hypothesis we will...
In hypothesis testing, which statement is true? A. if we reject the alternate hypothesis we will have proof of the null hypothesis. B. the null hypothesis will not be rejected unless the probability of observing the data provide convincing evidence that it is true. C. the null hypothesis will not be rejected unless the probability in the critical region is large. D. the null hypothesis will not be rejected unless the test statistic is larger (absolutely) than the critical value.
If we find that it is unlikely to observe the sample statistic that is actually observed...
If we find that it is unlikely to observe the sample statistic that is actually observed if the null hypothesis is true, then we should fail to reject the null hypothesis. reject the null hypothesis. reject the alternative hypothesis. calculate a new sample statistic.
When using inferential statistics, it is critical to have: More than one degree of freedom. A...
When using inferential statistics, it is critical to have: More than one degree of freedom. A truly random sample of the population. A binomial random variable A strong correlation with a Poisson distribution. A normally distributed population. The three ways of assessing probabilities are: Classical, Empirical, and Subjective Normal, Poisson, and Hypergeometric Type I, Type II, and Secular Binomial, Geometric, and a priori Global test, Histogram, and Stepwise If there are three, equally-likely events, the probability of each event occurring...
Indicate whether the following statement is true or false. If we do not reject the null...
Indicate whether the following statement is true or false. If we do not reject the null hypothesis, it is possible we have made both type I and type II errors. In an upper tail hypothesis test for the mean, the critical value is 2.575 and the test statistic is 2.5. In this case, the null hypothesis should not be rejected. The calculated p-value should be divided by 2 to make the decision for a two tail test. The sampling error...
1. Assumptions underlying the use of t-statistic in sample-based estimation are that the population is normally...
1. Assumptions underlying the use of t-statistic in sample-based estimation are that the population is normally distributed and population standard deviation is unknown. A. True B. False 2. The null hypothesis is rejected if the p-value (i.e., the probability of getting a test statistic at least as extreme as the observed value) is greater than the significance level. A. True B. False 3. When using the p-value to test hypotheses, the null hypothesis would be rejected if __________. A. the...
True or False: For all hypothesis tests, a small p-value means we will reject the null....
True or False: For all hypothesis tests, a small p-value means we will reject the null. True or False: If you are testing the means of two groups, then you would use ANOVA. True or False: A two-sample confidence interval must capture zero to show the groups are different. True or False: The test statistic for ANOVA is the f-statistic. True or False: For Chi-Square tests, if the observed counts and expected counts are extremely different, then we would have...
If the computed value of a chi-square statistic is less than the critical chi-square value, reject...
If the computed value of a chi-square statistic is less than the critical chi-square value, reject the null hypothesis at a predetermined Type I error rate. ANSWER: FALSE WHY IS THE ANSWER TO THIS FALSE? WHAT IS THE EXPLANATION?
A "sleep habits" survey answered by 46 randomly selected New Yorkers contained the question "How much...
A "sleep habits" survey answered by 46 randomly selected New Yorkers contained the question "How much sleep do you get per night?" The sample average was 7.8 hours, with a corresponding sample standard deviation of 0.82 hours. We want to test against the null hypothesis that New Yorkers get, on average, 8 hours of sleep per night. α=0.05. a. This null hypothesis should be formally written as: (You have two attempts at this question.) H0: μdifference = 8 H0: μ...
Which of the following is true with regard to a P-value? (More than one answer may...
Which of the following is true with regard to a P-value? (More than one answer may be correct.) a. The P-value is generated under the assumption that the null hypothesis is true. b. The P- value may be negative in some tests. c. If the P-Value is below 5% in a 5% significance level, then the null hypothesis will be rejected. d. In a left-tailed test if the P-Value is 100%, the sample statistic equals the population value as stated...
From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n...
From a random sample from normal population, we observed sample mean=84.5 and sample standard deviation=11.2, n = 16, H0: μ = 80, Ha: μ < 80. State your conclusion about H0 at significance level 0.01. Question 2 options: Test statistic: t = 1.61. P-value = 0.9356. Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is very strong. Test statistic: t = 1.61. P-value = 0.0644....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT